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Beliebt Rechnen >

integral of ((e^t+2e^{2t}))/(e^{3t)}

Lösung

\int \frac{( e ^{t} + 2 e ^{2 t} )}{e ^{3 t}} d t

Lösung

- \frac{1}{2} e^{- 2 t} - \frac{2}{e ^{t}} + C

Schritte zur Lösung

\int \frac{e ^{t} + 2 e ^{2 t}}{e ^{3 t}} d t

Multipliziere aus

\frac{e ^{t} + 2 e ^{2 t}}{e ^{3 t}} : \frac{1}{e ^{2 t}} + \frac{2}{e ^{t}}

= \int \frac{1}{e ^{2 t}} + \frac{2}{e ^{t}} d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{e ^{2 t}} d t + \int \frac{2}{e ^{t}} d t

\int \frac{1}{e ^{2 t}} d t = - \frac{1}{2} e^{- 2 t}

\int \frac{2}{e ^{t}} d t = - \frac{2}{e ^{t}}

= - \frac{1}{2} e^{- 2 t} - \frac{2}{e ^{t}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} e^{- 2 t} - \frac{2}{e ^{t}} + C

Graph

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